What question did this study set out to answer?

This research aims to explore quark and lepton flavor mixing through a structural framework based on division-algebra towers.

February 2, 2026Open Access

From Division-Algebra Towers to Quark and Lepton Flavor: CKM and PMNS from Corner Selection

Key Points

This research aims to explore quark and lepton flavor mixing through a structural framework based on division-algebra towers.
Derived parameters for quark mixing from a vacuum idempotent and corner projector in C⊗H⊗O.
Extended the framework to lepton mixing through geometrical selections in an axis+plane setup.
Utilized specific equations to predict mixing parameters and compared them with Particle Data Group values.
Derived the Cabibbo parameter λ as approximately 0.2236, closely matching the PDG value.
Calculated the hierarchy parameter A as approximately 0.816, slightly differing from the PDG value of 0.826.
Estimated the CP phase δ as approximately 64°, aligning well with the PDG value of 65.7° ± 1.5°.

Abstract

Two companion manuscripts presenting a structural approach to quark and lepton flavor mixing from division-algebra towers. "From Division-Algebra Towers to Quark Flavor Invariants: CKM from a Corner Selection" (33 pages) — derives the Cabibbo parameter λ = 1/ (2√5) ≈ 0. 2236, the hierarchy parameter A = √ (2/3) ≈ 0. 816, and the CP phase δ ≈ 64° from a vacuum idempotent and corner projector P₂ in C⊗H⊗O. "Lepton Mixing from Tower Geometry: A PMNS-Oriented Note" (8 pages) — extends the framework to leptons, showing that large PMNS mixing arises from a different orbit selection in the same axis+plane geometry. Key predictions: - λ = 1/ (2√5) = 0. 22361 (PDG: 0. 22501 ± 0. 00068) - A = √ (2/3) = 0. 8165 (PDG: 0. 826) - δ = π/2 − 2θC ≈ 64. 2° (PDG: 65. 7° ± 1. 5°) Associated code and numerical scripts available at DOI: 10. 5281/zenodo. 18364857

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